Combine the sugar and water in a saucepan over medium heat. Stir gently until the sugar dissolves completely, then stop stirring and let the mixture boil until it turns a deep amber color, about 5-7 minutes.
Remove the caramel from heat and carefully whisk in the heavy cream. Continue whisking until the mixture is smooth and glossy, then set aside to cool slightly.
Pour the warm caramel sauce into a bowl and let it cool to room temperature. This helps prevent melting the ice when blending.
Place the crushed ice into a blender. Add the cooled caramel sauce over the ice.
Blend on high speed until the mixture becomes slushy and smooth, about 30-45 seconds. You should see a glossy, pale gold texture with small ice crystals.
Pour the caramel ice slush into glasses, ensuring a generous scoop in each.
Serve immediately for the best icy texture, with a caramel drizzle or a sprinkle of sea salt if desired.
